How Do You Find Entropy for a Material Given Specific Equations?

[lifeonfire]

Homework Statement

For a material given by U=C₁PV² and PV²=C₂T
Find the entropy

Homework Equations

dS/dU = 1/T; dU/dV = -P

I don't know if I require anything else

The Attempt at a Solution

So from 2 equations I got U = C₁
C₂T

But dU/dT is not equal to S. Which equation do I use to get the entropy? I was thinking of using F = U-TS. Which will give F = C₁PV² - TS And then doing dF/dT but then I didn't use the 2nd condition at all.

What am I missing?

 

[I like Serena]

Hi lifeonfire!

Your relevant equations are not always true, the first requires V to remains constant, while the second requires S to remain constant.

For reversible processes, the equation dU=TdS-PdV is true without conditions on state variables.
From this you can isolate dS, apply the formulas given for your material, and integrate.